Question

A retailer buys cases of 24 shirts for $30/case and then resells them in packs of 5 for $8/pack. If the retailer sold all the shirts it purchased and profited $84 on the sale, how many packs of shirts did it sell?

Answer 1

We have been given that a retailer buys cases of 24 shirts for $30/case and then resells them in packs of 5 for $8/pack.

Further, we know that retailer sold all the shirts he purchased and profited $84 on the sale.

Let us first find LCM of 24 and 5. The LCM is 120.

Now, let us assume that the retailer bought 120x shirts. Therefore total profit will be:

$\text{Profit=}(24x)(8)-(5x)(30)\\\text{Profit=}192x-150x\\\text{Profit=}42x$

We can set this equal to the given profit to figure out the value of x first.

$42x=84\Rightarrow x=2$

Therefore, the retailer sold 120(2)=240 shirts, that is, 48 packs.

Answer 2

The retailer sells $\boxed{\bf 48\text{\bf\ packs}}$ of shirts.

Further explanation:

Cost price is the price at which an article is purchased.

Selling price is the price at which an article is sold.

If cost price is more than the selling price than loss occurs.

If selling price is more than the cost price then profit occurs.

Calculation:

It is given that a retailer buys cases of $24\text{ shirts}$ for $\ \ 30/\text{ case}$.

Then, the cost price (CP) of each shirt is calculated as follows:

$\begin{aligned}\text{CP}&=\dfrac{30}{24}\\&=\dfrac{10}{8}\\&=\dfrac{5}{4}\end{aligned}$  

Also, given that he resells them in packs of $5$ for $\ \ 8/\text{ pack}$.

Then, the selling price (SP) of each shirt is calculated as follows:

$\text{SP}=\dfrac{8}{5}$

Therefore, the profit is calculated as follows:

$\begin{aligned}\dfrac{8}{5}-\dfrac{5}{4}&=\dfrac{(8\cdot 4)-(5\cdot 5)}{20}\\&=\dfrac{32-25}{20}\\&=\dfrac{7}{20}\end{aligned}$  

Also, given that if the retailer sold all the shirts it purchased and profited $\ \ 84$ on the sale.

Therefore, the total number of shirts $(p)$ retailer solds is calculated as follows:

$\begin{aligned}p&=\dfrac{84}{(\frac{7}{20})\\&=\dfrac{84\cdot 20}{7}\\&=\dfrac{1680}{7}\\&=240}\end{aligned}$

 

Therefore, the number of packs $(n)$ he sold is calculated as follows:

$\begin{aligned}n&=\dfrac{240}{5}\\&=48\end{aligned}$  

Thus, the total number of packs retailer sold is $\boxed{\bf 48}$.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Profit and Loss

Keywords: Cost price, selling price, profit, loss, percentage, discount, marked price, compound interest.